Advanced LIGO [1]} and Advanced Virgo [2]} are gravitational-wave detectors, instruments designed to measure tiny spacetime distortions called gravitational waves.
These extreme-sensitive instruments are capable of detecting strain amplitudes smaller than e-23  and have observed gravitational waves from distinct systems such as binary black holes, binary neutron stars, and neutron star - black hole [3]}, [4]}, [5]}. However, such sensitivity can be overwhelmed by intrinsic noises or local environment noises coupling into the instrument [6]}, [7]}, [8]}. One common noise affecting the sensitivity of gravitational-wave detectors is scattered-light noise [9]}. It originates when a fraction of laser light is undesirably scattered, reflected from moving surfaces, and recombined in any of the detectors' optical cavities [10]}. Scattered-light noise (or scattering) manifests as arches in the detector's output with a frequency given by:
\(f_{\text{arch}}(t)=\frac{2N}{\lambda }|v_{\text{surface}}(t)|\) 
